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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Borsuk-Ulam theorems for arbitrary $ S\sp{1}$ actions and applications

Authors: E. R. Fadell, S. Y. Husseini and P. H. Rabinowitz
Journal: Trans. Amer. Math. Soc. 274 (1982), 345-360
MSC: Primary 55M20; Secondary 58E05
MathSciNet review: 670937
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Abstract: An $ {S^1}$ version of the Borsuk-Ulam Theorem is proved for a situation where Fix $ {S^1}$ may be nontrivial. The proof is accomplished with the aid of a new relative index theory. Applications are given to intersection theorems and the existence of multiple critical points is established for a class of functional invariant under an $ {S^1}$ symmetry.

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Keywords: Equivariant cohomology, index theory, Borsuk-Ulam Theorem, intersection theorems, minimax, critical point, Hamiltonian system
Article copyright: © Copyright 1982 American Mathematical Society